1. Field of the Invention
The invention relates generally to the field of estimating material properties of porous media. More specifically, the invention relates to methods for estimating such properties using computer tomographic (CT) images of porous media such as subsurface rock formation.
2. Background Art
Estimating material properties such as effective elastic moduli and attenuation of the elastic waves has substantial economic significance. Methods known in the art for identifying the existence of subsurface hydrocarbon reservoirs, including seismic surveying and well log analysis, need to be supplemented with reliable methods for estimating how fluids disposed in the pore spaces of the reservoir rock formations affect the elastic and attenuating properties of the rock to aid in interpretation of such surveys.
One method known in the art for estimating fluid transport properties is described in U.S. Pat. No. 6,516,080 issued to Nur. The method described in the Nur patent includes preparing a “thin section” from a specimen of rock formation. The preparation typically includes filling the pore spaces with a dyed epoxy resin. A color micrograph of the section is digitized and converted to an n-ary index image, for example a binary index image. Statistical functions are derived from the two-dimensional image and such functions are used to generate three-dimensional representations of the rock formation. Boundaries can be unconditional or conditioned to the two-dimensional n-ary index image. Desired physical property values are estimated by performing numerical simulations on the three-dimensional representations. For example, permeability is estimated by using a Lattice-Boltzmann flow simulation. Typically, multiple, equiprobable three-dimensional representations are generated for each n-ary index image, and the multiple estimated physical property values are averaged to provide a result.
In performing the method described in the Nur patent, it is necessary to obtain samples of the rock formation and to prepare, as explained above, a section to digitize as a color image. Economic considerations make it desirable to obtain input to fluid transport analysis more quickly than can be obtained using prepared sections. Recently, devices for generating CT images of samples such as drill cuttings have become available. Such CT image generating devices (CT scanners) typically produce three-dimensional gray scale images of the samples analyzed in the scanner. Such gray scale images can be used essentially contemporaneously as drill cuttings are generated during the drilling of a wellbore through subsurface rock formations.
Using images of samples of rock formations it is possible to obtain estimates of petrophysical parameters of the imaged rock sample, for example, porosity, permeability, shear and bulk moduli, and formation resistivity factor.
Seismic (or elastic) waves attenuate as they propagate through rock formations in the Earth's the subsurface. Attenuation means that the amplitude (of stress or deformation) of such waves decreases as the wave travels a certain distance through the rock formations. A formal definition of attenuation is as follows.
An attenuation coefficient α is defined as the exponential decay coefficient of an elastic wave:A(x)=A0 exp[−αx]  (1)
where A is the amplitude of the elastic wave; A0 is the original (unattenuated) wave amplitude; and x is the distance traveled by the elastic wave.
Another important quantity related to attenuation is the inverse quality factor Q−1, which is related to a by the expression:Q−1=αV/πf,  (2)
where V is the velocity (speed) of the elastic wave and f is its frequency.
Knowing attenuation is important for purposes of seismic imaging of the Earth's subsurface. Attenuation information is used during seismic processing to equalize the magnitude of a seismic signal at varying distances from the seismic energy source. Recently, it has been also used to better delineate formations with hydrocarbons. Typically, attenuation is larger in gas- or oil-bearing subsurface formations than in rock formations having only water in the pore spaces thereof (called “wet rock”). To quantify the interpretation of such effects and improve seismic imaging, a quantitative estimate of attenuation (Q−1) is desirable for a given type of formation.
A traditional method of measuring attenuation is in a laboratory where a physical sample of the rock formations of interest is placed between a sound source (transducer) and an acoustic receiver. An elastic impulse is generated by the transducer and its arrival is detected by the receiver. The amplitudes of both, the input acoustic energy (A0) and the detected acoustic energy (A(L)), are measured. Then Q−1 can be calculated from Equations (1) and (2) by the expression:
                                          Q                          -              1                                =                                    -                              1                L                                      ⁢                          V                              π                ⁢                                                                  ⁢                f                                      ⁢            ln            ⁢                                          A                ⁡                                  (                  L                  )                                                            A                0                                                    ,                            (        3        )            
where L is the length of the acoustic energy path through the rock sample. Other methods of calculating Q−1 from a physical experiment are known in the art.
To better understand the methodology of the present invention, it is important to describe the physical nature of attenuation of elastic waves.
Seismic energy dissipates in porous rock with fluid in the pore spaces due to wave-induced oscillatory cross-flow of the pore fluid. The viscous-flow friction irreversibly transfers part of the acoustic energy into heat. This cross-flow can be especially strong in partially saturated rock (rock having a combination of oil, and/or gas and water in the pore spaces) where the viscous fluid phase (water) moves in and out of, e.g., gas-saturated pore space. Such viscous friction losses may also occur in wet rock where elastic heterogeneity is present. Deformation due to a stress wave is relatively strong in the softer portion of the pore space of rock and is weak in the stiffer portion. The spatial heterogeneity in the deformation of the solid rock formation “frame” forces the fluid to flow between the softer and stiffer portions of the rock. Such cross-flow may occur at all spatial scales. Such cross-flow is known in the art as “squirt-flow.” Microscopic “squirt-flow” is developed at the sub-millimeter pore scale because a single pore may include compliant crack-like and stiff equi-dimensional parts.
It is important to understanding this invention to understand a link between attenuation and the elastic moduli of porous rock. Both attenuation and the elastic moduli are frequency-dependent. If the frequency of the elastic wave is low, the deformation of the pore space is relatively slow. Slow pore space deformation means that the pore fluid can freely travel between the soft and stiff pores without resisting wave-induced deformation. The elastic moduli at low frequency are thus relatively low. If the frequency of the elastic wave is very high, however, the pore fluid cannot freely travel between the soft and stiff pores because the rate of wave-induced deformation is high and the fluid is relatively viscous (as related to the wave frequency). This means that at high frequency, the soft and stiff pores are in effect hydraulically disconnected. The fluid in the soft pores has no space to move and, therefore, resists the deformation as the equivalent of an elastic (rather than fluid) body. This effect makes the elastic moduli at high frequency relatively high.
It appears that Q−1 reaches a maximum at intermediate frequencies, these frequencies generally believed to occur at the transition from the low-frequency to high-frequency pore fluid behavior, as described above. The transition point (“transition frequency”) is essentially impossible to obtain other than using complex laboratory experiments on samples of the rock because of the very complex pore geometry of the natural pore space.
There exists a need to use images such as the foregoing CT scan images to estimate certain elastic-wave-related properties of rock formations, in particular the maximum Q−1.